A schematic would help.
TLDNR; An analog switch might work.
First, let's look at what you are doing here. I presume youare also connecting the ground of your external 3.3V supply to the emitter aswell (and thus also to the "0-volt" pin on your PSU's connector).This will work because the two supplies are isolated. Generally speaking, youreally do not know WHAT is on those two pins of the PSU connector. It's aremote on/off, and an NPN is not a relay.
I presume you are doing something like in the circuit below,which only works because the external 3.3V on the base will turn on thetransistor and allow charge carriers to flow from collector to emitter, thuscompleting the circuit between your external connector with ~4V and 0V nodes.With the 0V node at GND, it's not a problem since the GND is floating withrespect to the GND of your larger PSU that your are trying to turn on.
However, it will not work when you try to use the same 3.3Vfrom the same PSU because you are likely causing a connection between the 0Vnode and the real PSU GND, thus the 0V node is no longer floating, but isgrounded. You may only be reading that terminal node at 0V simply because it isa high impedance input to a control circuit, and that input needs to be raisedto approx. 4V from the other terminal in order to turn on your PSU. As soon asyou try to use the same 3.3V from the same PSU it will be grounded and willnever be able to be raised to 4V as needed to turn it on.
And everything I've said above is speculation based on whatyou've described.
If you have a schematic of that PSU then you will knowexactly what those two pins are, and perhaps can come up with a good way toturn them on. Otherwise. it's just what we in the industry call a contactclosure. We use a relay or a hard switch to connect those two terminals to turnon the PSU.
As an alternative, you might be able to use the 3.3VSB(stand-by) power from your PSU to power an analog switch like the well-knownCD4066 (74LVQ4066 in 3.3V). The switch might be able to complete the circuitwhile maintaining isolation from the 3.3VSB power. Analog switches have twoback-to-back N and P channel MOSFETS and source and drain are"isolated" from gate and substrate, and only the gates and substratesare referenced to the chip's power supply itself.
Finally, it would be best to know where exactly those twoterminals are going to inside your PSU, and how are they connected. This iswhere a schematic of your PSU really helps. Without that, you're flying blindhere.